 | 582 pages
...ol two unequal lines, 13 equal to the rectangle contained by their sum and difference. SECTION III. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Is this proposition true, if the base bo greater than a semicircle? If so, why has Euclid omitted it... | |
 | Francis James Jameson - 1851 - 144 pages
...extremity of a diameter at right angles to it, each will be a tangent to the second circle. 1848. (A), The angle at the centre of a circle is double of the...that is, upon the same part of the circumference, (in. 20.) (E). If two straight lines AEB, CED, in a circle, intersect in E, the angles subtended by... | |
 | 1851 - 382 pages
...of a given circle, 3. Prove that the diameter of a circle is the greatest chord, .... 4. Prove that the angle at the centre of a circle is double of the angle at the circumference, upon the same base, .... 5. Explain how the height of an inaceessibl object may be determined, . 6. What are the five regular... | |
 | Charles Astor Bristed - 1852 - 470 pages
...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. 5. In a circle, the angle in a semicircle is a right angle ; but the angle in a segment greater than... | |
 | Royal Military Academy, Woolwich - 1853 - 400 pages
...centre; that is, the centre is in CA. Therefore, if a straight line, etc. QED PROPOSITION XX. THEOR. The angle at the centre of a circle is double, of...that is, upon the same part of the circumference. BOOK III. PROF. XX., XXI. First, let E, the centre of the circle, be within the angle BAC, and join... | |
 | Euclides - 1853 - 146 pages
...5. The centre of the circle is in CA. Therefore, if a straight line, &e. QEU PROP. XX. — THEOREM. The angle at the centre of a circle is double of the...that is, upon the same part of the circumference. Let ABC be a circle, and BEC an angle at the centre, and BAC an angle at the circumference, which have... | |
 | University of Sydney - 1853 - 134 pages
...the straight line intercepted without the triangle between the perpendicular and the obtuse angle. 8. The angle at the centre of a circle is double of the angle at the circumference upon the same base. Prove this, and thence shew that the angle in a semi circle is a right angle. 9. Two circles intersect... | |
 | Dugald Stewart - 1854 - 536 pages
...different quantities, and the connexions which exist between different relations. When we demonstrate that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles... | |
 | Dugald Stewart - 1854 - 538 pages
...different quantities, and the connexions which exist between different relations. When we demonstrate that the angle at the centre of a circle is double of the angle at the circumference on the same base, we ascertain a relation between two quantities. When we demonstrate that triangles... | |
 | John Hind - 1855 - 540 pages
...centre of the circle circumscribing the triangle ABC, we have OA=OB= ОС = the radius R : then, since the angle at the centre of a circle is double of the angle at the circumference upon the same base, we have, from Article (77), REGULAR POLYGONS. From this, it appears that the sine of any angle of a... | |
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The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference. 
